If `x gt0` and g is bounded function then `lim_(xtooo)(f(x)e^(nx)+g(x))/(e^(nx)+1)`

If x gt0 and g is bounded function then lim_(ntooo)(f(x)e^(nx)+g(x))/(e^(nx)+1)

Evaluate lim_(xtooo) (log_(e)x)/(x)

Evaluate lim_(xtooo) (log_(e)x)/(x)

Evaluate lim_(xtooo) (log_(e)x)/(x)

Let function f be defined as f:R^(+)toR^(+) and function g is defined as g:R^(+)toR^(+) . Functions f and g are continuous in their domain. Suppose, the function h(x)=lim_(ntooo)(x^(n)f(x)+x^(2))/(x^(n)+g(x)), x gt0 . If h(x) is continuous in its domain,then f(1).g(1) is equal to (a) 2 (b) 1 (c) 1/2 (d) 0

Let function f be defined as f:R^(+)toR^(+) and function g is defined as g:R^(+)toR^(+) . Functions f and g are continuous in their domain. Suppose, the function h(x)=lim_(ntooo)(x^(n)f(x)+x^(2))/(x^(n)+g(x)), x gt0 . If h(x) is continuous in its domain,then f(1).g(1) is equal to

Let f(x)=g(x)(e^(1//x) -e^(-1//x))/(e^(1//x) + e^(-1//x)) , where g is a continuous function then lim_(x to 0) f(x) exist if

Using the L .Hospital rule find limits of the following functions : lim_(xtooo) x^(1//In(e^(x)-1)

lim_(x-gt0) (e^(3x)-1)/(log(1+5x))

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then